Integral equations for the Fourier‐transformed boundary values for the transmission problems for right‐angled wedges and octants
E. Meister
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Source: Crossref
Published: Jan 1, 1986
DOI: 10.1002/mma.1670080112
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Abstract A 4×4‐system of integral equations for the Fourier transformed boundary values of the normal derivatives of the wave functions defined in the four quadrants of R 2 ‐space is derived. This system results from the scalar transmission problem with continuous passage of the boundary values of the total wave‐fields and of the weighted normal derivatives corresponding to the case of magnetically polarized fields. Several equivalent systems of integral equations are deduced then which show that Banach's fixed point principle may be applied at least for slightly differing media in the four quadrants. The method, which is equivalent to a compatibility condition for holomorphic functions, may be generalized to the case of the scalar transmission problem for octants in R 3 ‐space. There a 12 × 12‐system of integral equations for the Fourier transformed normal derivatives on the quarter‐plane faces is established.
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